Tilings of the Sphere with Right Triangles II: The $(1,3,2)$, $(0,2,n)$ Subfamily

Robert J. MacG. Dawson, Blair Doyle

Abstract

Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper shows that no right triangles in a certain subfamily can tile the sphere, although multilayered tilings are possible.